The balanced chemical equation for the reaction of sodium silicate (Na₂SiO₃) with hydrofluoric acid (HF) to produce hexafluorosilicic acid (H₂SiF₆), sodium fluoride (NaF), and water (H₂O) is:

Na₂SiO₃ + 6HF → H₂SiF₆ + 2NaF + 3H₂O

Here's how the equation is balanced:

* Sodium (Na): 2 Na atoms on the left side and 2 Na atoms on the right side.

* Silicon (Si): 1 Si atom on the left side and 1 Si atom on the right side.

* Oxygen (O): 3 O atoms on the left side and 3 O atoms on the right side.

* Hydrogen (H): 6 H atoms on the left side and 6 H atoms on the right side.

* Fluorine (F): 6 F atoms on the left side and 6 F atoms on the right side.

This reaction is a highly exothermic reaction, meaning it releases a lot of heat. It's important to note that hexafluorosilicic acid is a strong acid and should be handled with caution.